scholarly journals On the Gorenstein Property of the Associated Graded Ring and the Rees Algebra of an Ideal

1993 ◽  
Vol 155 (2) ◽  
pp. 397-414 ◽  
Author(s):  
A. Ooishi
Keyword(s):  
Rees Algebra ◽  
Associated Graded Ring ◽  
Graded Ring

scholarly journals Depth formulas for certain graded rings associated to an ideal

1994 ◽  
Vol 133 ◽  
pp. 57-69 ◽  
Author(s):  
Sam Huckaba ◽  
Thomas Marley
Keyword(s):  
Local Ring ◽  
Rees Algebra ◽  
Graded Rings ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
The Relationship

In this paper, we investigate the relationship between the depths of the Rees algebra R[It] and the associated graded ring grI(R) of an ideal I in a local ring (R, m) of dimension d > 0. Hereand.

scholarly journals Action of finite groups on Rees algebras and Gorensteinness in invariant subrings

1999 ◽  
Vol 42 (2) ◽  
pp. 393-401
Author(s):  
Shin-Ichiro Iai
Keyword(s):  
Finite Group ◽  
Local Ring ◽  
Finite Groups ◽  
Rees Algebra ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Gorenstein Rings ◽  
Rees Algebras ◽  
Stable Ideal ◽  
A Finite Group

Let G be a finite group of order N and assume that G acts on a Cohen-Macaulay local ring A as automorphisms of rings. Let N be a unit in A. For a given G-stable ideal I in A we denote by R(I) = ⊕n≥0In and = G(I) = ⊕n≥0In/In+1 the Rees algebra and the associated graded ring of I, respectively. Then G naturally acts on R(I) and G(I) too. In this paper the conditions under which the invariant subrings R(I)G of R(I) are Cohen-Macaulay and/or Gorenstein rings are described in connection with the corresponding ring-theoretic properties of G(I)G and the a-invariants a(G(I)G of G(I)G. Consequences and some applications are discussed.

On the Buchsbaumness of the Associated Graded Ring of a One-Dimensional Local Ring

2009 ◽  
Vol 37 (5) ◽  
pp. 1594-1603 ◽  
Author(s):  
M. D'Anna ◽  
M. Mezzasalma ◽  
V. Micale
Keyword(s):  
Local Ring ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
One Dimensional
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